Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory

• URL: http://arxiv.org/abs/2604.20333v1
• Date: Wed, 22 Apr 2026 08:29:35 GMT
• Title: Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory
• Abstract summary: High-capacity associative memories based on Kernel Logistic Regression (KLR) are known for their exceptional performance but are hindered by high computational costs.<n>This paper investigates the compressibility of KLR-trained Hopfield networks to understand the geometric principles of its robust encoding.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: High-capacity associative memories based on Kernel Logistic Regression (KLR) are known for their exceptional performance but are hindered by high computational costs. This paper investigates the compressibility of KLR-trained Hopfield networks to understand the geometric principles of its robust encoding. We provide a comprehensive geometric theory based on spontaneous symmetry breaking and Walsh analysis, and validate it with compression experiments (quantization and pruning). Our experiments reveal a striking contrast: the network is extremely robust to low-precision quantization but highly sensitive to pruning. Our theory explains this via a ``sparse function, dense representation'' principle, where a sparse input mapping is implemented with a dense, bimodal parameterization. Our findings not only provide a practical path to hardware-efficient kernel memories but also offer new insights into the geometric principles of robust representation in neural systems.

Related papers

• Contraction, Criticality, and Capacity: A Dynamical-Systems Perspective on Echo-State Networks [13.857230672081489]
  We present a unified, dynamical-systems treatment that weaves together functional analysis, random attractor theory and recent neuroscientific findings.<n>First, we prove that the Echo-State Property (wash-out of initial conditions) together with global Lipschitz dynamics necessarily yields the Fading-Memory Property.<n>Second, employing a Stone-Weierstrass strategy we give a streamlined proof that ESNs with nonlinear reservoirs and linear read-outs are dense in the Banach space of causal, time-in fading-memory filters.<n>Third, we quantify computational resources via memory-capacity spectrum, show how
  arXiv  Detail & Related papers  (2025-07-24T14:41:18Z)
• Stochastic Fractional Neural Operators: A Symmetrized Approach to Modeling Turbulence in Complex Fluid Dynamics [0.0]
  We introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role.<n>Our approach provides theoretical guarantees for the approximation quality and suggests that these neural operators can serve as effective tools in the analysis and simulation of complex systems.
  arXiv  Detail & Related papers  (2025-05-12T13:11:08Z)
• A Sampling Theory Perspective on Activations for Implicit Neural Representations [73.6637608397055]
  Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. We conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding.
  arXiv  Detail & Related papers  (2024-02-08T05:52:45Z)
• Scalable Neural Network Kernels [22.299704296356836]
  We introduce scalable neural network kernels (SNNKs), capable of approximating regular feedforward layers (FFLs) We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.
  arXiv  Detail & Related papers  (2023-10-20T02:12:56Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint [48.25573695787407]
  We prove that large ConvResNets can not only approximate a target function in terms of function value, but also exhibit sufficient first-order smoothness. Our theory partially justifies the benefits of using deep and wide networks in practice.
  arXiv  Detail & Related papers  (2022-06-09T15:35:22Z)
• Great Truths are Always Simple: A Rather Simple Knowledge Encoder for Enhancing the Commonsense Reasoning Capacity of Pre-Trained Models [89.98762327725112]
  Commonsense reasoning in natural language is a desired ability of artificial intelligent systems. For solving complex commonsense reasoning tasks, a typical solution is to enhance pre-trained language models(PTMs) with a knowledge-aware graph neural network(GNN) encoder. Despite the effectiveness, these approaches are built on heavy architectures, and can't clearly explain how external knowledge resources improve the reasoning capacity of PTMs.
  arXiv  Detail & Related papers  (2022-05-04T01:27:36Z)
• Hyperbolic Neural Networks++ [66.16106727715061]
  We generalize the fundamental components of neural networks in a single hyperbolic geometry model, namely, the Poincar'e ball model. Experiments show the superior parameter efficiency of our methods compared to conventional hyperbolic components, and stability and outperformance over their Euclidean counterparts.
  arXiv  Detail & Related papers  (2020-06-15T08:23:20Z)
• Constant-Expansion Suffices for Compressed Sensing with Generative Priors [26.41623833920794]
  We prove a novel uniform concentration for random functions that might not beschitz but satisfy a relaxed notion of Lipe-theoreticalness. Since the WDC is a fundamental concentration inequality inequality of all existing theoretical guarantees on this problem, our bound improvements in all known results in the heart on with priors, including one, low-bit recovery, and more.
  arXiv  Detail & Related papers  (2020-06-07T19:14:41Z)
• Understanding Generalization in Deep Learning via Tensor Methods [53.808840694241]
  We advance the understanding of the relations between the network's architecture and its generalizability from the compression perspective. We propose a series of intuitive, data-dependent and easily-measurable properties that tightly characterize the compressibility and generalizability of neural networks.
  arXiv  Detail & Related papers  (2020-01-14T22:26:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.